Periodicity and blowup in a two-species cooperating model

In this paper, the cooperating two-species Lotka–Volterra model is discussed. The existence and asymptotic behavior of T -periodic solutions for the periodic reaction diffusion system under homogeneous Dirichlet boundary conditions are first investigated. The blowup properties of solutions for the same system are then given.

It is shown that periodic solutions exist if the intra-specific competitions are strong whereas blowup solutions exist under certain conditions if the intra-specific competitions are weak. Numerical simulations and a brief discussion are also presented in the last section.